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Revealing physical interactions in complex systems from observed collective dynamics constitutes a fundamental inverse problem in science. Current reconstruction methods require access to a system's model or dynamical data at a level of…
Numerous social, medical, engineering and biological challenges can be framed as graph-based learning tasks. Here, we propose a new feature based approach to network classification. We show how dynamics on a network can be useful to reveal…
Network models have been widely used to study diverse systems and analyze their dynamic behaviors. Given the structural variability of networks, an intriguing question arises: Can we infer the type of system represented by a network based…
This paper presents the foundation for a decomposition theory for Boolean networks, a type of discrete dynamical system that has found a wide range of applications in the life sciences, engineering, and physics. Given a Boolean network…
Dynamic networks consist of interconnected dynamical systems. The subsystems can be viewed as transformations of input signals into output signals, where signals flow from one system into another through interconnections. The signal flows…
A major achievement in the study of complex networks is the observation that diverse systems, from sub-cellular biology to social networks, exhibit universal topological characteristics. Yet this universality does not naturally translate to…
One of the basic frameworks in science views behavioral products as a process within a dynamic system. The mechanism might be seen as a representation of many instances of centralized control in real time. Many real systems, however,…
Interactions between units in phyical, biological, technological, and social systems usually give rise to intrincate networks with non-trivial structure, which critically affects the dynamics and properties of the system. The focus of most…
Natural physical, chemical, and biological dynamical systems are often complex, with heterogeneous components interacting in diverse ways. We show how simple graph neural networks can be designed to jointly learn the interaction rules and…
Empirical studies of graphs have contributed enormously to our understanding of complex systems. Known today as network science, what was originally a theoretical study of graphs has grown into a more scientific exploration of communities…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
What can we learn from the collective dynamics of a complex network about its interaction topology? Taking the perspective from nonlinear dynamics, we briefly review recent progress on how to infer structural connectivity (direct…
Statistical properties of binary complex networks are well understood and recently many attempts have been made to extend this knowledge to weighted ones. There is, however, a subtle difference between networks where weights are continuos…
Complex systems such as ecological communities and neuron networks are essential parts of our everyday lives. These systems are composed of units which interact through intricate networks. The ability to predict sudden changes in the…
An important part of the analysis of bio-molecular networks is to detect different functional units. Different functions are reflected in a different evolutionary dynamics, and hence in different statistical characteristics of network…
Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…
Networks effectively capture interactions among components of complex systems, and have thus become a mainstay in many scientific disciplines. Growing evidence, especially from biology, suggest that networks undergo changes over time, and…
Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…
It is a fundamental challenge to understand how the function of a network is related to its structural organization. Adaptive dynamical networks represent a broad class of systems that can change their connectivity over time depending on…
A fundamental premise of statistical physics is that the particles in a physical system are interchangeable, and hence the state of each specific component is representative of the system as a whole. This assumption breaks down for complex…